That, however, was as close as they ever got on a racecourse and so it was left to racing’s international panel of handicappers to determine which of the two was the outstanding horse in a memorable year. When their decision was published on Tuesday, it was emphatic. American Pharoah, with a final rating of 134, was 4lb clear of Golden Horn, who was in turn another 4lb ahead of Treve, the Arc winner in 2013 and 2014. Shared Belief, who died of colic in December, was a second US-trained horse in the top three, rated the equal of Treve on 126.

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Some, perhaps many, racing fans, in Europe in particular, may disagree or point out that American Pharoah, like all but a tiny handful of US-trained horses, raced on the controversial anti-bleeding medication Lasix throughout his career. Yet the scale of his achievement in becoming the 12th Triple Crown winner is undeniable while the form of his final and most impressive success, in the Breeders’ Cup Classic was franked a few weeks later when Effinex, the six-and-a-half-length runner-up, took the Grade One Clark Handicap.

Nor is there any doubt that, between them, American Pharoah and Golden Horn dominated racing on either side of the Atlantic. American Pharoah recorded three of the top five individual performances of 2015, in the Classic (134), the Haskell Invitational (130) and the Belmont Stakes (129), while Golden Horn, in the Derby and Eclipse (both 130), was responsible for the other two. Treve’s easy win in the Prix Vermeille (126) the only other victory in Europe rated above 125

Ahmed Zayat, Bob Baffert and Victor Espinoza, respectively the owner, trainer and jockey of American Pharoah, were all present at a ceremony in London on Tuesday to see their colt named the Longines World’s Best Racehorse for 2015.

“Not only was he brilliant on the racetrack, he connected with everyone in America,” Zayat said. “For 37 years, we were waiting for a horse like that and he was finally the one. What I want everyone to remember about American Pharoah is not only was he majestic and brilliant in the way he raced and how much he liked winning the way he did, [it] is how much he was the people’s horse.”

Baffert said that American Pharoah “was the kind of horse who was unique and I could let him do that and share him; and to me that was fun. I was his trainer but I was also a big fan. It was so uplifting for the people of America.” Epinoza, meanwhile, summed up the Triple Crown winner very simply. “Every time I sat on him, it was like I was in the clouds.”

At a press conference which followed the publication of both the international classifications and Europe’s juvenile rankings, Phil Smith, the British Horseracing Authority’s senior handicapper, paid tribute to the talent and consistency of both American Pharoah and Golden Horn.

“They both kept their form remarkably well,” Smith said. “Golden Horn raced in four different countries, though he didn’t quite log as many miles [in the air] as American Pharoah. Looking back at his form in the Derby, it really worked out this year, as the second horse, Jack Hobbs, went on to win [the Derby] in Ireland. It was as good as his performance shortly afterwards in the Eclipse,” said Smith

“American Pharoah was the champion in three categories [eight to nine furlongs, 10 furlongs and 12 furlongs] and Golden Horn was the champion in two.”

There was never a realistic chance that American Pharoah and Golden Horn would meet on the track, or race on as four-year-olds given their immense value as stallions.

“It’s a shame that more three-year-olds don’t stay in training,” Phil Smith, the British Horseracing Authority’s senior handicapper said later, at a press conference following the publication of both the international classifications and Europe’s juvenile rankings. “If you look at Frankel, he was rated 126 as a two-year-old, 136 as a three-year-old and 140 as a four-year-old. Who is to say how far those horses could have gone?

“As a racing enthusiast, I’d love to see more of these horses kept in training, not just for European racing but for world racing. American Pharoah’s last performance was his best performance, so who can say he would not have progressed ever further at four if he was still improving?”

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His rating is the joint-highest of the last five years alongside Dawn Approach, who took the 2,000 Guineas and St James’s Palace Stakes as a three-year-old. In all, only three juveniles – Frankel, New Approach and Dream Ahead – have earned a higher rating in the last 12 years, and all were Group One winners at three.

“There have been only four or five two-year-olds in recent years who were good enough to win three Group Ones in the season,” Mark Bird, the handicapper responsible for Irish juveniles, said, “so he is in good company with the likes of Arazi and Zafonic and more recently, Fasliyev and Johannesburg.

“[But] there are no guarantees as to what he may or may not achieve as a three-year-old. Only five or six of the top 20 last year went on to improve their ratings as three-year-olds. It will be interesting to see whether he fails to train on, like Johannesburg, or goes on like Zafonic or a horse like [O’Brien’s] St Nicholas Abbey.”